Fire temperature

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Fire temperature - time relations

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Ser

TH1

N21d

no*

1579

c. 2

BLDG

National Research

Conseil national

1

*

1 Council Canada

de rechenhes Canada

Institute for

lnstitut de

Research in

recherche en

Construction

construction

-

Time Relations

by T.T.

Lie

Appeared in

The SFPE Handbook of Fire Protection Engineering 1988

Section 3, Chapter 5

p. 3-81

-

3-87

(IRC Paper No. 1579)

Reprinted with permission

NRCC

30108

i

I R C

-r ITfSf

(3)

ABSTRACT

Analytical expressions are given that describe characteristic temperature curves as a

function of the significant parameters for various fire conditions commonly met with in

practice. Expressions

are

also given for the standard fire curve used

in

North America and

for the fire curve adopted by the International Organization for Standardization

(ISO).

The

curves

are

intended as basic fire exposure curves for

fire

_{resistive design.}

L'auteur prdsente des expressions analytiques ddcrivant les courbes de temp6rature

caract6ristiques en fonctiP-

'

-

% >

-

'-

---gnditions d'incendie

que l'on retrouve coura

ons concernant la

courbe d'incendie stand

courbe d'incendie

adoptde par lYOrganisat

rbes

d'exposition

(4)

Section

3lChapter

5 FIRE TEMPERATURE-

TIME RELATIONS

INTRODUCTION

The intensity and duration of fire in buildings can vary

in

a wide range. and several studies have been carried out to investigate the determining factors. At present it is possible to estimate the temperature course of fire in enclosures under various conditions, provided the values of the parameters that determine it are known.

Several of these parameters. however, such as amount and surface area of the combustible materials, are unpredictable as they change with time and often vary from compartment to compartment

in

a building. It is not possible. therefore. to know at the time a building is erected the temperature course of a fire to which objects

in

that building might be exposed during its service life.

-

It

is possible, however, to indicate for any enclosure a

temperature-time curve that. with reasonable likelihood. will not be exceeded during the lifetime of the building. Such curves are useful as a basis for the fire-resistive design of buildings. They can also facilitate studies of fire resistance of building components exposed to fires of various intensity and duration.

In

this chapter, analytical expressions will

be

given that describe characteristic temperature curves as a function of the significant parameters for various fire conditions commonly met with in practice.

Expressions will also be given for the standard fire curve used in North America, and for the fire curve adopted by the International Organization for Standardization (ISO).

FIRE TEMPERATURES

The temperature course of a fire in an,enclosure may be divided into three periods:

I.

The growth period.

2.

The fully developed period. and

3.

The decay period.

Dr. T.T. Lie is Research Officer with the Institute for Research in Construction, National Research Council of Canada. He has carried out research related to fire resistance design, which includes evalu- ation of the fire resistance of building constructions by calculation and testing. o

t

GROWTH DEVELOPED PERIOD 0 I 2 3 4-- TIME. h

Fig. 3-5.1. ldeali=ed temperature course of

firr.

These periods are illustrated in Figure

3-5.1,

where an idealized fire temperature course is shown. During the growth period, heat produced by the burning materials is accumulated in the enclosure. As a result. other materials may be heated so severely that they also ignite. At this stage of the fire, the gas temperatures rise very quickly to high values. The rather sudden ignition of materials in all parts of the room is called "flash over." After the flash over. the fully developed period starts. Because the temperatures

in

the enclosure are relatively low in the growth period. their influence on the fire resistance of structural members is negligible.

In

fire resistance studies. therefore. the growth period can be disregarded. Actual risk of failure of structural members or fire seuarations begins when the fire reaches the fully developed stage. In this itage. temperatures of about

1000°C or higher can be reached. and the heat transferred from the fire to structural members may substantially reduce their strength. This risk also exists

in

the decay period.

Parameters Determining the Fire

Temperature Course

The most important parameters that determine the temperature course of a fire were first shown by Kawagoe and Sekine' and by Odeen.' who estimated the heat balance for fires

in

enclosed spaces. Usually part of the heat produced during a fire in an enclosure will be absorbed by the walls and contents. a part by the gases. and a part will be lost

(5)

QR = RADIATION LOSSES

Q, = HEAT CONTENT OF INFLOWING AIR

QL = HEAT CONTENT OF OUTFLCWING GASES

= HEAT LOSSES TO THE WALLS

Qc = HEAT PRODUCED B Y COMBUSTION

QG = RISE OF THE HEAT CONTENT O F THE GASES _{I N THE ENCLOSURE}

Fig. 3-5.2. Hem W n c e for an enclosure during a Jim.

by radiation and convection from windows. (See Figure 3-5.2.) There is also loss o f chemical energy that could have been released as heat because of outflow of unburned gases. which bum outside the enclosure. I n addition. there is loss of unburned particles.

To be able to determine the temperature course. it is necessary to know at each moment during a fire. the rate at which heat is produced and the rate at which heat is lost to exposed materials and surroundings. Several of the parameters that determine heat production and heat losses. such as material properties, room dimensions. wall construction. window area. and emissivity of the flames and exposed materials. can be determined with reasonable accuracy. Others that are known approximately are the amount of gases that burn outside the room. the loss of unburned particles through windows. and the temperature differences in the room.

There are several parameters, however. whose magni- tude cannot be predicted. Usually they change with time. and therefore. their value at the time of occurrence of a fire is determined by chance. Such parameters include the amount. surface area. and arrangement of the combustible contents. velocity and direction o f wind. and the outside temperature. The influence o f wind.' and that of fire load can be substantial. Surveys show, for instance. that the vanabil- ity of fire loads in various types o f buildings is such that deviations in the order o f 50 percent or more from the most probable fire load are ~ o m m o n . ~ As a consequence. variabil- ity of fire load alone may easily cause deviations from the most probable temperature course of hundreds degrees centigrade in temperature and 50 percent or more in fire duration.

POSSIBLE FIRE SEVERITIES

Owing to the substantial influence of uncertain factors. i t i s impossible to predict accurately the temperatures to which building components will be exposed during their service life. Even i f the analysis to predict fire temperature

courses in enclosures i s perfect, i t is very improbable that a

1

certain predicted temperature course will occur.

The fire temperature to which building components will most likely be exposed during the use of a building i s the relatively low temperature of a fire that has been extin- guished before i t reaches the fully developed stage. There i s

a small although not insignificant change o f occurrence of a fully developed fire. I n this case, and assuming that the fire cannot be influenced by action of the fire brigade. the fire will be controlled either by the surface area of the materials that can participate in the burning or by the rate o f air supply through the openings.'.'

Whether the fire will be largely controlled by surface area or ventilation depends on the amount of combustible contents. Unless i t s quantity. surface area. and arrangement are controlled. or the size of the windows and floor area made such that the possibility o f a ventilation-controlled fire becomes

remote."^^

the type of fire that may occur i s

unpredictable. According to- statistical data. combustible contents of 10 to 60 kg per m- of floor area are normal, and there is a considerable probability of enclosures having a combustible content of 40 to 100 k g h ~ . ' . ~ I t is probable that

in the latter range. as confirmed by experiments..' the fire _I

will be mainly ventilation controlled, even when large window openings are present. I t is likely that the greater the

space behind the windows. or to a certain extent, the deeper i

the enclosure. the more material or surface area i t will contain and therefore the greater will be the probability o f a ventilation-controlled fire. Usually a ventilation-controlled fire is the more severe fire, and because of the substantial probability of .its occurrence. it is common to base fire resistance requirements for buiidings on the assumption that tire severities will be controlled by ventilation.

CHARACTERISTIC TE,MPERATURE

CURVES

I t is possible to indicate for any enclosure a characteristic temperature-time curve whose effect, with reasonable likelihood. will not be exceeded during the lifetime o f the building. Such curves are useful as a basis for the fire- resistance design of buildings. They can also facilitate studies o f fire resistance o f building components exposed to fires of different severity.

There are several reports which present the temperature course of fires in fully developed and decay

period^.'.'.^.^^'^

I n all of these studies a procedure is followed in which the fire temperatures are determined by solving a heat balance for the enclosure under consideration.

For the fully developed period and ventilation-controlled fires. there is reasonable agreement in the temperatures found in the various studies. except for rather shallow rooms of limited size. I n the latter case. the amount of combustible gases that burn outside may increase in such a way with increasing ventilation that the temperature de- creases.'

There i s less agreement in the results of the various studies for the decay period. partly due to the complexity of ,the processes that determine the temperature in that period. So far. rates of decay of temperature can only be established empirically or by making conservative or highly idealized assumptions. Because of the different approaches in deriving the rates o f decay. there is a rather wide spread in the results of the various studies. Fortunately the influence o f temperature variation in the decay period on the maximum temper-

(6)

FIRE TEMPERATURE-TIME

RELATIONS

3-83

1 1 *---- 200

0 1 2 3

TIME. h $2

Fig. 3-5.3. Tempemtun c w e s f w f i resistance design.

atures reached in building components is relatively small."

For the purpose of deriving a temperature-time curve that.

with reasonable probability, will not be exceeded during the

lifetime of the building,

it

will be sufficient to use a curve that

only approximately reflects the effect of heating in the decay

period. This is further explained in Figure

3-5.3.

In Figure

3-5.3

curve a illustrates a fire temperature

curve derived theoretically for a certain building. The prob-

ability of occurrence of a fire with a more severe effect than

shown by the curve is once in

50

years. Curve b illustrates a

fire temperature curve for the same building, but

it

is

assumed that the rate of burning remains constant until all

combustible materials are consumed, whereupon the fire

temperature drops linearly to room temperature. Although

curve b differs in shape from curve a, their heating effect is

approximately the same. If curve b is used instead of curve

a. the probability of occurrence of a more severe fire than

that represented by the relevant curve may change some-

what. for instance. from once in fifty years to somewhat

more or less than fifty years. In practice this means that

virtually the same fire safety will be provided whether curve

a or curve b is used for the fire-resistance design of a

building. The use of curve b instead of curve a has the

advantage that

it

is easier to define.

Expressions for Characteristic

Temperature Curves

In the following, analytical expressions are given that

describe characteristic temperature curves as a function of

the significant parameters for various fire conditions com-

monly met with in practice. For the fully developed period.

the derivation of these curves will be based on the temper-

ature curves for ventilation-controlled fires calculated ac-

cording to the method described by Kawagoe and Sekine.'

The temperatures attained in ventilation-controlled fires

are described (in addition'to the thermal properties of the

material bounding the enclosure) by a parameter, known as

the opening factor

F

where

A

is area of the openings in the enclosure, H is height

of the openings, and

A,

is area of the bounding surfaces

(walls and floor and ceiling). The method of calculating

A<H

for openings of unequal height is described in Refer-

ences 9 and

1 1.

The rate of burning, R, of the combustible materials in

the enclosure is given by

TABLE 3-5.1 Thermal Properties of the Enclosure

Factor

Description

k

Thermal

conductivity

of bounding material: 1.16

Wlm

K

for a

heavy material

( p 2

1600 kg/m3), 0.58

Wlm

K

for a light

material

(r i

1600 kg/mq

pc Volumetric

speclfic heat of bounding material: 2150

x 103

J/m3K for a heavy material

(p r

1600 kglmq,

1075

x lo3

J I ~ ~ K

for a light material

( p <

1600 kg/m3)

A,

Total inner surface area bounding the enclosure, including

window area:

1000 m2

H

Window heqht: 1.8

m

E

Emissivity for radiation transfer beween hot gases and inner

bounding surface of the enclosure:

0.7

a,

Coefficient of heat transfer by convection between fire and

inner bounding surface area:

23 W/m2K

a,

Coefficient of heat transfer between outer bounding surface

area and surroundings:

23 W/m2K

c

Specific heat of combustion gases: 1340 J/Nm%

G

Volume of combustion gas produced

by

burning

1

kg of

wood: 4.9 Nm3/kg

q

Heat released

in

the enclosure

by

buming

1

kg of

wood:

1o.n

x to6 kg

To

Initial temperature:

20%

V

Volume of enclosure:' 1000 m3

Ax

Thickness of elementary layers of bounding material: 0.03

m

At

Time increment: 0.0004167

hr

0

Thickness of bounding material: 0.1

5

m

I1 can tm shown Mat Me influence of the

volume

of the enclosure on the fire temperahm is

negligible.

and. thus, if Q is the fire load per unit area of the surfaces

bounding the enclosure, the duration of the fire.

T,

is

determined by

For given thermal properties of the material bounding

the enclosure, the heat balance can be solved for the

temperature as a function of the opening factor F. Besides

depending on F. the temperature course is also a function of

the thermal properties of the material bounding the enclo-

sure.

In this study, two materials have been chosen as repre-

sentative bounding materials: one with thermal properties

resembling those of a heavy material (high heat capacity and

conductivity) and one representing those of a light material

(low heat capacity and conductivity). The thermal properties

of these materials are given in Table

3-5.1.

In practice.

materials with a density of approximately

1600

kg/m2 or

more, e.g., normal-weight concretes, sand lime brick. and

most clay bricks, can be considered as belonging to the

group of heavy material. Those with a density of less than

1600

kg/m2. e.g., lightweight and cellular concretes and

plasterboard. can be regarded as belonging to the group of

light materials.

Using the method described in Reference

I

I, the tem-

perature course of fires in enclosures has been calculated for

the two chosen bounding materials and for various values of

the opening factor." The conditions for which the calcula-

tions have been performed are shown in Table

3-5.1

and the

(7)

3-84

DESIGN CALCULATIONS

A~

0 200

b i 6 j a 2

TIME. h

Fig. 3-5.4. Temperature-time curves for venti&uion-control&d/ins in enclosum boundsd by dominantly heavy morerials f p z 1600 k g l d ~ . calculated for wriaru opening factors by solving a heat balance for the enclosure.

curves in these figures were used as a basis for the derivation of temperature curves for fire-resistance design. It was found that these temperature curves could be reasonably described by the expression

where

T

= the fire temperature

in

"C,

r

= time

in

hr,

F

=

opening factor

in

m"', and C = a constant taking into account the influence of the properties of the boundary material on the temperature. C = 0 for heavy materials (p

r

1600 kg/m2), and C = I for light materials (p

<

1600 kg/m). The expression is valid for

and

If

t

>

(0.081R

+

I , a value oft = (0.08lF)

+

I should be used.

If

F >

0.15, a value of

F

= 0.15 should be used.

The temperature-time curves evaluated from Equation 4

and those obtained by solving the heat balance for the

8 TIME. h

Fig. 3-5.5. Tempemure-time curves for ventihion-controlled/ires in enclosures bounded by dominantly light materiais ( p < 1600 kglkglnr'). calculated for wriour opening factors by solving a heat bolonce for rhc enclosun.

T IME, h

Fig. 3-5.6. Compahon between temperature-time curves obtained by solving a heat balance and those described by an analytical expression for ventilorion-controlled /irrs in enclosures bounded by dominantly

heavy materials ( p 2 1600 k g l d ) .

enclosure are shown

in

Figures 3-5.6 and 3-5.7 for various values of the opening factor.

It is seen that with the aid of the analytical expression. temperature curves can be developed that reasonably describe the curves derived from solving the heat balance.

As discussed previously, the temperatures in the decay period are more difficult to calculate due to the complexity of the processes that determine the temperature in this period. On the other hand, if the temperature variations are not very large, the influence of such variations

in

the decay period on the temperature attained in exposed building components is

in

general relatively small. Therefore. describing the temperature course in the decay period by a temperature-time relation that approximately reflects the decrease of temperature in this period is sufficient.

According to experimental data of Kawagoeqhe rate of temperature decrease of a fire with a fully developed period of less than one hour is roughly 10°C per minute, and that of a fire with a fully developed period of more than one hour is P C per minute. The Swedish code assumes a rate of decrease of 10°C per minute irrespective of the duration of the fully developed period of the fire.9 A comparison with semi-empirical data developed by Magnusson and The- landersson9 shows that the assumption of a rate of decrease of 10°C per minute is too fast for fires of long duration an$ too slow for fires of short duration. According to Harmathy. who studied several experimental fires of relatively short d~ration,".'~ the rate of decrease of temperature for such fires is in the order of I5 to 20°C per minute.

-FROM HEAT BAIANCE

"' FROM ANALYTICAL EXPRESSION

TIME, h

Fig. 3-5.7. Compahon between tempemure-time curves ohained by solving a heat balance and those described by an analytical expression for venrihrion-controlled~es in enclosures bounded by dominantly light

(8)

FIRE TEMPERATURE-TIME RELATIONS

3-85

. -

TIME. h

Fig.3-5.8. Characteristic temperotwe curpes for w'ousfire loads, Q,

(opening factor, F

=

0.05 m'", heavy boundin# material).

In general, the longer the duration of the fully developed

period the lower the rate of decrease of temperature. Using

this information the following expressions have been derived

for the temperature course of fire in the decay period

with the condition

In the above equations T

=

fire temperature.

r =

time at

which the decay starts as given by Equation 3,

t =

time

under consideration

( t

>

r ) ,

and

T

=

temperature given by

Equation 4 at the time

t = 7.

The temperature curves obtained from Equations

4

and

7 are illustrated in Figure 3-5.8 for various fire loads and an

opening factor of 0.05 m''2. In Figure 3-5.9 the influence is

shown of the openings on the fire temperature course. It can

be seen that the fire load determines the duration of the fire,

whereas the openings determine both the duration and the

intensity of the fire. In Figure 3-5.10 a characteristic temper-

ature curve is compared with the temperatures measured at

several places in a room during an experimental fire.'

It

is

seen that the curve developed from the analytical expression

reasonably characterizes the temperatures obtained during

the experimental fire. It is somewhat conservative but satis-

factory to use as a design curve for fire resistance.

STANDARD

FIRE CURVE

In studies of fire resistance. it is common to expose

building elements to heating in accordance with a standard

LARGE OPENING ~ A L I un 800 3 I-

2

600 W a

;

400 0 0

I

1 2 3

:

?

TIME. h

Fig. 3-5.9. Influence of opening factor on

firr

temperature course.

'"1

,

j:w"

'

0 0.5 1 . 0 1.5 2.0 2.5 3.0 3.5 4 2 '

TIME, h

Fig. 3-5.10. Comparison of design temperature curves derived from a d y t i c d expressions with temperatures measured during an expmti- mentallfn @ load per unit internal area of the bounding

surfaces

Q

=

18.75 kg/', opening factor F

=

0.047 m'", heavy bounding m a t e d ) .

temperature-time relation. The standard temperature-time

curves used in various countries are shown in Figure 3-5.11.

It

can be seen that there are no significant differences

between the various standard curves. The values of the

curve adopted by ISO" are given in Table 3-5.2. Those used

in North America'" are given in Table 3-5.3.

There are also analytical expressions for several of the

standard curves. The expression that describes the IS0

curve is

where

t =

tiine

in

minutes.

T

=

fire temperature in

"C,

and

To

=

initial temperature

irl

"C.

For the curve used in North America, several analytical

expressions exist." One of the expressions is of the form of

a sum of exponential functions

where a ,

=

532 for "C. 957 for

O F ; a2 =

-

186 for "C. -334 for

OF:

a, =

820 for "C, 1476 for

O F ; a, =

-0.6;

a, =

-3;

a, =

-12.

4 0 0 ~ 1 1 3 4 5 8 7 8

DURATION, h

Fig. 3-5.1 1. Standcvd lfre temperature-time relations used in various countries for testing of building elements.

(9)

1

ABLE 3-5.2 Standard Temoerature-Time Relatlon Accordina to IS0 834" Time Temperature "F Temperature

"C

Time Temperature "F Temperature

"C

The extreme deviation from the values given

in

Table

3-5.2 are -26°C at 45 min; +48"C at 3.5 hours; and -78°C at

8 hours.

This form is suitable for use in analytical heat flow calculations, because when it is used as a boundary condition the heat transfer equations are integrable.

A set of expressions that more accurately approximate the values given in Table 3-5.2 is

where a , = 580 for "C. 1044 for OF: a2 = -276.8 for "C.

-498.2 for OF; a, = 714.4 for "C, 1286 for O F : a, = 0.8429;

a,

*

0.9736;

a,

= 8.910.

The maximum duration of the temperature, given by Equations 11, 12. and

13,

from the values tabulated in Table

3-5.2 is -7'C at 40 min.

Another temperature-time relation. given

in

Reference

18, has the form

7-To=a,

tanha,t+a,tanha,t+a,tanha,t, t < 2 ( 1 1 )

T

-

To

= all

-

exp (-3.795534)]

+

3 0 6 . 7 4 4 (14)

T

-

To

-

906.7

+

41.671, t 2 2 for "C (12)

T

-

To

= 1632

+

751, t 2 2 for

"F

(13) TABLE 3-5.3 Standard Fire Temperstunr-77me

Relation Used in North America (NFPA No. 2511'"

Temperature rise

Time in Minutes . of fire ("C)

0 0 5 556 10 659 15 71 8 30 821 60 925 90 986 120 1.029 180 1,090 240 1.133 360 1.193

where a = 750 for "C, 1350 for OF: and t = time in minutes. This expression is frequently used and is a reasonably accurate approximation of the relation between temperature and time given

in

Table 3-5.2.

NOMENCLATURE

area of the openings in the enclosure. m2 area of the internal bounding surfaces. m' constant

opening factor, m"'

height of openings in the enclosure. rn

fire load per unit area of the internal bounding surfaces. kg/m2

rate of burning, kglhr fire temperature, "C

fire temperature at the time r, "C time. hr

(10)

FIRE TEMPERATURE-TIME RELATIONS

3-87

REFERENCES

I. K. Kawagoe and T. Sekine. "Estimation of Fire Temperature- Time Curve in Rooms." B.R.I. Orcusionul Reporr No. I I . Build- ing Research Institute, Ministry of Construction. Tokyo ( 1%3).

2 . K. Odeen. "Theoretical Study of Fire Characteristics in En- closed Spaces," Blrllerin 10. Division of Building Construction. Royal Institute of Technology. Stockholm 11963).

3. P.H. Thomas and A.J.M. Heselden. "Fully Developed Fires in Single Companments." Fire Research Note N O . 923. Building Research Establishment. Fire Research Station. Borehamwood (1972).

4. T.T. Lie. Fire and Blrildings, Applied Science Publishers Lim- ited. London. pp. 19-22 ( 1972).

5.

P.H.

Thomas. A.J.M. Heselden. and M. Law, "Fully Devel-

oped Companment Fires; Two Kinds of Behavior." Fire Re- search Technical Paper N o . 18. Her Majesty's Stationery Office. London ( 1967).

6. T.T. Lie. Fire and Buildings, Applied Science Publishers Lim- ited. London ( 1972). pp. 9- 1 1.

7. T.Z. Harmathy, "A New Look at Compartment Fires, Part I

and Pan 11." Fire Tech.. 8. 3 and 4 (1972).

8. K. Kawagoe, "Fire Behavior in Rooms." Reporr N o . 21. Building Research Institute. Ministry of Construction, Tokyo (1958).

9. S.E. Magnusson and S. Thelandenson, "Temperature-Time Curves of Complete Process of Fire Development. Theoretical Study of Wood Fuel Fires in Enclosed Spaces." Acta Polytech-

nica Scandinavia. Civil Engineering and Building Construction Series No. 65. Stockholm (1970).

Y. Tsuchiya and K. Sumi. "Computation of the Behavior of Fire in an Enclosure." Comb. ilnd Flume. 16 (1971).

K . Kawagoe. "Estimation of Fire Temperature-Time Curve in Rooms." Reseurclr Paper N o . 29. Building Research Institute. Japan ( 1967).

T.T. Lie. "Characteristic Temperature Curves for Various Fire Severities," Fire Tech., 10. 4 ( 1974).

E.G. Butcher. T.B. Chitty, and L.A. Ashton. "The Tempera- tures Attained by Steel in Building Fires," Fire Research Technical Puper No. 14, Her Majesty's Stationery Office, London ( 1966).

E.G. Butcher. G.K. Bedford, and P.J. Fardell. "Further Exper- iments on Temperatures Reached by Steel in Buildings," Sym- posilrm N o . 2. Behavior of Srrucrural Steel in Fire. Paper N o . I .

Her Majesty's Stationery Office. London ( 1968).

"Fire Resistance Tests-Elements of Building Construction."

lnrcrnarionul Standard I S 0 834. ( 1975).

NFPA 251. Standard Methods of Fire Tests of Building Con- srrucrion and Materials. National Fire Protection Association. Quincy, MA ( 1985).

G. Williams-Leir. "Analytical ~ ~ u i v a l e n - t s of Standard Fire Temperature Curves," Fire Tech.. 9. 2 (1973).

J.P.

Fackler, "Concernant la Resistance au Feu des Elements

de Construction." Cahier 299, Centre Scientifique et Technique du Batiment ( 1959).